Can someone plz draw a diagram for what the triangle should look like??

Thanks

So I came across this question in my test and got it wrong..I assumed the equilateral triangle has the greatest area and marked root3/4
Now i see the logic..any triangle drawn by the above specifications will have two legs as the radius..we have to maximise the area so the third leg should be the largest.

However,is this some kind of a theoram/fact that we should be knowing?That to get the largest area of a triangle,the triangle has to be a right angle and not an equilateral one?

uptowngirl92 wrote:So I came across this question in my test and got it wrong..I assumed the equilateral triangle has the greatest area and marked root3/4
Now i see the logic..any triangle drawn by the above specifications will have two legs as the radius..we have to maximise the area so the third leg should be the largest.

However,is this some kind of a theoram/fact that we should be knowing?That to get the largest area of a triangle,the triangle has to be a right angle and not an equilateral one?

You can do it with calculus and set the derivative of area with respect to height to 0 and solve for the base in terms of height, which will be at maximum area. Turns out base = twice height which only occurs when its a 45,45,90 triangle, which with two legs of length 1 has an area of 1/2

Calculus is not tested..........